Sökning: "Sobolev capacity"
Hittade 5 avhandlingar innehållade orden Sobolev capacity.
1. Sobolev-Type Spaces : Properties of Newtonian Functions Based on Quasi-Banach Function Lattices in Metric Spaces
Sammanfattning : This thesis consists of four papers and focuses on function spaces related to first-order analysis in abstract metric measure spaces. The classical (i.e., Sobolev) theory in Euclidean spaces makes use of summability of distributional gradients, whose definition depends on the linear structure of Rn. LÄS MER
2. Capacities, Poincaré inequalities and gluing metric spaces
Sammanfattning : This thesis consists of an introduction, and one research paper with results related to potential theory both in the classical Euclidean setting, as well as in quite general metric spaces.The introduction contains a theoretical and historical background of some basic concepts, and their more modern generalisations to metric spaces developed in the last 30 years. LÄS MER
3. Newtonian Spaces Based on Quasi-Banach Function Lattices
Sammanfattning : The traditional first-order analysis in Euclidean spaces relies on the Sobolev spaces W1,p(Ω), where Ω ⊂ Rn is open and p ∈ [1, ∞].The Sobolev norm is then defined as the sum of Lp norms of a function and its distributional gradient.We generalize the notion of Sobolev spaces in two different ways. LÄS MER
4. Boundary Value Problems for Nonlinear Elliptic Equations in Divergence Form
Sammanfattning : The thesis consists of three papers focussing on the study of nonlinear elliptic partial differential equations in a nonempty open subset Ω of the n-dimensional Euclidean space Rn. We study the existence and uniqueness of the solutions, as well as their behaviour near the boundary of Ω. LÄS MER
5. Integral inequalities of Hardy and Friedrichs types with applications to homogenization theory
Sammanfattning : This PhD thesis deals with some new integral inequalities of Hardy and Friedrichs types in domains with microinhomogeneous structure in a neighborhood of the boundary. The thesis consists of six papers (Paper A -- Paper F) and an introduction, which put these papers into a more general frame and which also serves as an overview of this interesting field of mathematics. LÄS MER